The ability to guarantee a single homogeneous liquid phase is a key consideration in computer-aided mixture/blend design (CAMbD). In this article, we investigate the use of a classifier surrogate of the phase stability condition within a CAMbD optimisation model for designing solvent mixtures with guaranteed phase stability properties. We show how to develop such classifiers for describing multiple candidate mixtures over a range of compositions and temperatures based on the generation of phase stability data using thermodynamic models such as UNIFAC. We test the approach on two solvent design case studies and illustrate its effectiveness in enabling the in silico design of stable mixtures, simultaneously providing a probability of phase stability as an interpretable metric.

Asserting phase stability entails the global solution of a nonconvex optimisation problem, typically the tangent plane distance minimisation (TPDM). To improve computational tractability, we propose classifier-based surrogate models to replace the TPDM. We seek models that represent several multicomponent mixtures simultaneously, across various component identities, temperatures, and compositions. We investigate both artificial neural networks (ANN) and support vector machines (SVM) and use Matthew's correlation coefficient (MCC) as performance metric for the corresponding binary classification problems. For SVM models, linear, polynomial, and radial basis function (RBF) kernels are assessed; while for ANNs, the tanh and relu activation functions are investigated. We test the performance of these surrogate models on a set of ternary mixtures that involve ibuprofen and two solvents with fixed or variable temperatures. The results show that ANNs and SVMs can both predict phase stability reliably, with RBF-SVM giving the lowest computational cost.

This paper revisits the approach of transforming a mixed-integer polynomial program (MIPOP) into a mixed-integer quadratically-constrained program (MIQCP), in the light of recent progress in global solvers for this latter class of models. We automate this transformation in a new reformulation engine called CANON, alongside preprocessing strategies including local search and bounds tightening. We conduct comparative tests on a collection of 137 MIPOPs gathered from test libraries such as MINLPLib. The solver GUROBI gives the best performance on the reformulated MIQCPs and outperforms the generic global solvers BARON and SCIP. The MIQCP reformulation also improves the performance of SCIP compared to direct MIPOP solution, whereas the performance of BARON is comparable on the original MIPOPs and reformulated MIQCPs. Overall, these results establish the effectiveness of quadratic reformulation for MIPOP global optimization and support its integration into global solvers.

Mixed-integer polynomial programs (MIPOPs) frequently arise in chemical engineering applications such as pooling, blending and operations planning. Many global optimization solvers rely on mixed-integer linear (MIP) relaxations of MIPOPs and solve them repeatedly as part of a branch-and-bound algorithm using commercial MIP solvers. GUROBI, one of the prominent MIP solvers, recently added the capability to solve mixed-integer quadratically-constrained quadratic programs (MIQCQPs). This paper investigates global optimization of MIPOPs via their reformulation as MIQCQPs followed by their solution to global optimality using GUROBI. The effectiveness of this approach is tested on 60 instances of MIPOPs selected from the library MINLPLib. The performance of the MIQCQP reformulation approach is compared to the state-of-the-art global solvers BARON, ANTIGONE and SCIP in GAMS. For the case of single threading, a reduction of 28% and 42% compared to SCIP and ANTIGONE respectively is observed. This approach, therefore, holds promise for integration into existing global solvers to handle MIPOPs.